The present invention pertains to an automotive vehicle brake system providing brake slip control and traction slip control. A brake system of this type is known from German Published Patent Application No. 36 35 846. In order to minimize the number of valves required for traction slip control, it is there suggested to provide a locking valve in each connection line from the pressure medium storage reservoir to the tandem master cylinder if the brake circuit associated with this connection line has a driven wheel. During a traction slip control phase, the locking valves are closed and, via a pump, pressure is built up in the brake circuit of the driven wheel while the locking valve prevents pressure medium from escaping into the storage reservoir. In these systems, only one such locking valve is required in the case of a one-axle drive and of a front-axle/rear-axle brake circuit allocation. In this case, this single locking valve is required for the brake circuit of the driven axle. For all-wheel drive vehicles and for vehicles with diagonal brake circuit allocation, one valve is not sufficient since both brake circuits have driven wheels. The arrangement and number of the valves required thus depends on the number of driven wheels as well as on brake circuit allocation.